Much of our time in 8th grade is spend analyzing the characteristics of linear functions. Linear functions are very useful in the “real world,” and understanding how they work is an important key to understanding any relationship between two changing quantities.

A linear equation has four parts: an independent variable, a dependent variable, **slope** and a **y-intercept**. Students are first introduced to these parts through the use of slope-intercept form.

In 8th grade, the equation **y = mx + b** is most often used to represent linear functions. The variable *x* represents an input value, and the variable *y* represents an output value. The variable *m*, represents the rate of change between the inputs and outputs, or the **slope** of the relationship.

We first investigate slope of a graph, by measuring the differences horizontally and vertically between two points.

We then move to finding those differences between two points by using subtraction.

Finally, we use the *slope formula* to calculate the slope without having to use a graph.

Don’t think we forgot about the last part of a linear function! The y-intercept is simply the coordinates of the point where the graphed line crosses the y-axis. It is represented by the *b* in slope-intercept form.

To learn more about slope, click here. Try finding slope from a graph here, and slope from two points here. Try identifying the parts of a linear equation in slope intercept form here. Good luck!

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I understood how to do this very well with the slope intercept form.

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I remember how to change equations from slope intercept form to standard form and back again.

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I understand how to do all of this very well.

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I remember finding the difference between two points and how to use the slope formula, y=mx+b.

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